What is a PRP ?
A PRP is a probable prime number, a number that nobody knows how to prove
or disprove its primality.
Here are some criterions that can be used to recognize these numbers
:
- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N
should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3.
N should pass the strong test in base b.
- or more (if someone has got an idea) !!!
Submit your PRPs
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See the Latest PRPs
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| Rank |
Probable prime |
Digits (> 50000) |
Who ? |
When ? |
| 9001 | (7*10^100737+71)/3 | 100738 | Robert Price | 05/2018 |
| 9002 | (24737*2^334628+1)/3 | 100737 | Lelio R Paula | 07/2014 |
| 9003 | 15^85639-28 | 100720 | Lelio R Paula | 10/2016 |
| 9004 | 27068^5259+5259^27068 | 100718 | Hans Havermann | 08/2018 |
| 9005 | 2^334562+577294575 | 100711 | Lelio R Paula | 09/2016 |
| 9006 | 4*3^211077-5 | 100710 | Lelio R Paula | 08/2014 |
| 9007 | 2^334524+145 | 100702 | Lelio R Paula | 07/2009 |
| 9008 | (2^334451+714)/2 | 100680 | Stefano Morozzi | 09/2020 |
| 9009 | 27648^4375+4375^27648 | 100666 | Hans Havermann | 09/2018 |
| 9010 | (1017*2^334391-1)/3535 | 100662 | Lelio R Paula | 05/2015 |
| 9011 | (2^334309+3122)/2 | 100637 | Stefano Morozzi | 09/2020 |
| 9012 | 2^334294-113111 | 100633 | Enzo Doria | 07/2014 |
| 9013 | 25581^8582+8582^25581 | 100626 | Hans Havermann | 08/2018 |
| 9015 | 6^129308-17723 | 100622 | Enzo Doria | 03/2013 |
| 9014 | (19*10^100627+287)/9/292157 | 100622 | Alfred Reich | 11/2022 |
| 9016 | 6^129305+95 | 100619 | Lelio R Paula | 10/2016 |
| 9017 | 2^334244-1167 | 100618 | Lelio R Paula | 09/2016 |
| 9018 | (2^334233+3066)/2 | 100614 | Stefano Morozzi | 09/2020 |
| 9019 | (76*10^100611+77)/9 | 100612 | Robert Price | 10/2019 |
| 9020 | 7*10^100606-93 | 100607 | Robert Price | 08/2020 |
| 9021 | (26*10^100566+49)/3 | 100567 | Robert Price | 08/2019 |
| 9022 | (21*2^334050+1)/935 | 100558 | Lelio R Paula | 12/2013 |
| 9023 | 24885^10984+10984^24885 | 100555 | Hans Havermann | 07/2018 |
| 9024 | (1351^32119-1)/1350 | 100551 | Serge Batalov | 06/2022 |
| 9025 | (78557*2^334018+1)/4326021 | 100548 | Lelio R Paula | 07/2014 |
| 9026 | (35*10^100542+1)/9 | 100543 | Serge Batalov | 11/2010 |
| 9027 | 23578^18367+18367^23578 | 100538 | Hans Havermann | 07/2018 |
| 9028 | 13^90251+24 | 100535 | Lelio R Paula | 10/2016 |
| 9029 | 2^333963+789 | 100533 | Lelio R Paula | 08/2011 |
| 9030 | 2^333919-1840087 | 100520 | Enzo Doria | 06/2015 |
| 9031 | (2^333916+1698)/2 | 100519 | Stefano Morozzi | 09/2020 |
| 9032 | 2^333911+72623 | 100518 | Enzo Doria | 04/2016 |
| 9033 | 24605^12168+12168^24605 | 100517 | Hans Havermann | 08/2018 |
| 9034 | 66*10^100502+7 | 100504 | Robert Price | 07/2020 |
| 9035 | 18^80064-67 | 100503 | Lelio R Paula | 10/2016 |
| 9036 | (13*10^100487+137)/3 | 100488 | Robert Price | 06/2021 |
| 9037 | 23034^23034-12085^12085 | 100483 | Serge Batalov | 04/2024 |
| 9038 | 5^143742-48 | 100472 | Lelio R Paula | 10/2016 |
| 9039 | 24095^14784+14784^24095 | 100472 | Hans Havermann | 08/2018 |
| 9040 | 2^333757-112123 | 100471 | Enzo Doria | 06/2014 |
| 9041 | (7953^25759-1)/7952 | 100470 | Serge Batalov | 06/2022 |
| 9042 | 23030^23030-7401^7401 | 100464 | Serge Batalov | 04/2024 |
| 9043 | 7*10^100457-57 | 100458 | Robert Price | 06/2020 |
| 9044 | 27358^4693+4693^27358 | 100444 | Hans Havermann | 07/2018 |
| 9045 | 8*10^100439-51 | 100440 | Robert Price | 08/2019 |
| 9046 | 2^333603-108861 | 100425 | Enzo Doria | 03/2014 |
| 9047 | 9*7^118818-2 | 100414 | Lelio R Paula | 11/2014 |
| 9048 | 2^333546-17097 | 100408 | Enzo Doria | 05/2013 |
| 9049 | (19*10^100403+287)/9/3 | 100403 | Alfred Reich | 11/2022 |
| 9050 | 17^81597+72 | 100401 | Lelio R Paula | 10/2016 |
| 9051 | (3613^28219-1)/3612 | 100396 | Serge Batalov | 06/2022 |
| 9052 | p(20559)#/2+8 | 100384 | Robert Price | 01/2017 |
| 9053 | 11^96390-24 | 100380 | Lelio R Paula | 10/2016 |
| 9054 | 23011^23011+18846^18846 | 100373 | Serge Batalov | 04/2024 |
| 9055 | (2^333385+2730)/2 | 100359 | Stefano Morozzi | 09/2020 |
| 9056 | 4832563059*2^333333+30029 | 100353 | Donovan Johnson | 01/2008 |
| 9057 | 23565^18136+18136^23565 | 100353 | Hans Havermann | 07/2018 |
| 9058 | 2^333354+763 | 100350 | Lelio R Paula | 08/2011 |
| 9059 | (1608961*2^333333+1)/3 | 100349 | Alex_soldier | 09/2022 |
| 9060 | (424517*2^333333+1)/5 | 100349 | Alex_soldier | 09/2022 |
| 9061 | (887087*2^333333+1)/5 | 100349 | Alex_soldier | 09/2022 |
| 9062 | (1159703*2^333333+1)/7 | 100349 | Alex_soldier | 09/2022 |
| 9063 | (25*10^100343-67)/3 | 100344 | Robert Price | 06/2019 |
| 9064 | 2^333289-109483 | 100330 | Enzo Doria | 04/2014 |
| 9065 | 2^333240-2790209 | 100316 | Enzo Doria | 03/2016 |
| 9066 | 23601^17798+17798^23601 | 100314 | Hans Havermann | 05/2018 |
| 9068 | (2^333227-2^166614+1)/5 | 100311 | | 11/2006 |
| 9067 | 2^333225+719 | 100311 | Lelio R Paula | 08/2011 |
| 9069 | 2^333221-2785333 | 100310 | Enzo Doria | 10/2015 |
| 9070 | 76^53332-75 | 100308 | Norbert Schneider | 02/2015 |
| 9071 | (29*10^100302+583)/9 | 100303 | Robert Price | 06/2021 |
| 9072 | 6^128892-17573 | 100298 | Enzo Doria | 03/2013 |
| 9073 | (47*10^100283-119)/9 | 100284 | Robert Price | 05/2019 |
| 9074 | 2^333105-113215 | 100275 | Enzo Doria | 07/2014 |
| 9075 | (31*2^333102+1)/2375 | 100272 | Lelio R Paula | 11/2013 |
| 9076 | 4*10^100257-83 | 100258 | Robert Price | 10/2018 |
| 9077 | 17^81476-74 | 100253 | Lelio R Paula | 10/2016 |
| 9078 | 23392^19207+19207^23392 | 100199 | Hans Havermann | 06/2018 |
| 9079 | (2^332830+750)/2 | 100192 | Stefano Morozzi | 09/2020 |
| 9080 | (206*10^100189-17)/9 | 100191 | Robert Price | 01/2020 |
| 9081 | 17^81417-16 | 100180 | Theodore Burton | 11/2005 |
| 9082 | (2^332773+590)/2 | 100175 | Stefano Morozzi | 09/2020 |
| 9083 | 2*23^73562+215 | 100172 | Eric Chen | 08/2023 |
| 9085 | 2^332739-113215 | 100165 | Enzo Doria | 07/2014 |
| 9084 | (19*31^67163-199)/30 | 100165 | Eric Chen | 04/2024 |
| 9086 | 2^332730-1865621 | 100162 | Enzo Doria | 03/2016 |
| 9087 | 91^51127-2 | 100160 | Lelio R Paula | 09/2013 |
| 9088 | 15^85159-32 | 100155 | Lelio R Paula | 10/2016 |
| 9089 | 22963^22963+4620^4620 | 100143 | Serge Batalov | 04/2024 |
| 9090 | 22960^22960+9991^9991 | 100128 | Serge Batalov | 04/2024 |
| 9091 | 6^128661+97 | 100118 | Lelio R Paula | 10/2016 |
| 9092 | 19^78285+40 | 100108 | Lelio R Paula | 07/2016 |
| 9093 | 6^128640+5 | 100102 | Lelio R Paula | 11/2014 |
| 9094 | 10^100095+89973 | 100096 | Patrick De Geest | 10/2022 |
| 9095 | 10^100095-400001 | 100095 | Robert Price | 09/2021 |
| 9096 | 10^100095-203693 | 100095 | Patrick De Geest | 10/2022 |
| 9097 | 22779^22970-22970^22779 | 100093 | Norbert Schneider | 08/2020 |
| 9098 | (2^332468+3130)/2 | 100083 | Stefano Morozzi | 09/2020 |
| 9099 | (14*10^100075+61)/3 | 100076 | Robert Price | 12/2018 |
| 9100 | (2^332435+3098)/2 | 100073 | Stefano Morozzi | 09/2020 |
| 9101 | 28562^3189+3189^28562 | 100072 | Hans Havermann | 05/2018 |
| 9102 | 10^100053+56193 | 100054 | Alexander Weiss | 04/2024 |
| 9103 | 6^128565-127 | 100044 | Lelio R Paula | 08/2016 |
| 9104 | (2^332317+2106)/2 | 100038 | Stefano Morozzi | 09/2020 |
| 9106 | 2^332309-133 | 100035 | Lelio R Paula | 02/2011 |
| 9107 | 2^332307+731 | 100035 | Lelio R Paula | 07/2011 |
| 9105 | 937^33662-33662^937 | 100035 | Norbert Schneider | 05/2023 |
| 9108 | 2^332301+12927 | 100033 | Lelio R Paula | 04/2013 |
| 9109 | 17025^23642-23642^17025 | 100032 | Norbert Schneider | 04/2024 |
| 9110 | 23406^18781+18781^23406 | 100031 | Hans Havermann | 04/2018 |
| 9111 | 2^332277-4573 | 100026 | Yves Minet | 03/2019 |
| 9112 | 12^92684-13 | 100023 | Lelio R Paula | 07/2016 |
| 9113 | 70^54207-54207^70 | 100018 | Norbert Schneider | 04/2023 |
| 9114 | 78557*2^332193+55669 | 100005 | Jorge Menendez | 04/2019 |
| 9115 | 78557*2^332192+72689 | 100005 | Jorge Menendez | 04/2019 |
| 9116 | 10^100003+45799 | 100004 | Stefano Morozzi | 04/2019 |
| 9117 | 10^100003+155461 | 100004 | Stefano Morozzi | 04/2019 |
| 9118 | 10^100003+211389 | 100004 | Stefano Morozzi | 04/2019 |
| 9119 | 10^100003+381027 | 100004 | Stefano Morozzi | 04/2019 |
| 9120 | 10^100003+540703 | 100004 | Stefano Morozzi | 04/2019 |
| 9121 | 10^100003+823977 | 100004 | Stefano Morozzi | 04/2019 |
| 9133 | 10^100002+236023 | 100003 | Stefano Morozzi | 05/2018 |
| 9134 | 10^100002+433741 | 100003 | Stefano Morozzi | 05/2018 |
| 9122 | 2^332202+104659 | 100003 | Stefano Morozzi | 04/2019 |
| 9123 | 2^332202+857539 | 100003 | Stefano Morozzi | 04/2019 |
| 9124 | 2^332202+181773 | 100003 | Stefano Morozzi | 04/2019 |
| 9125 | 2^332202+687543 | 100003 | Stefano Morozzi | 04/2019 |
| 9126 | 2^332202+941595 | 100003 | Stefano Morozzi | 04/2019 |
| 9127 | 2^332202+445813 | 100003 | Stefano Morozzi | 04/2019 |
| 9128 | 2^332202+1599727 | 100003 | Stefano Morozzi | 04/2019 |
| 9129 | 2^332202+1389567 | 100003 | Stefano Morozzi | 04/2019 |
| 9130 | 2^332202+1206315 | 100003 | Stefano Morozzi | 04/2019 |
| 9131 | 2^332202+1958647 | 100003 | Stefano Morozzi | 04/2019 |
| 9132 | 10^100003-562857 | 100003 | Patrick De Geest | 07/2019 |
| 9135 | (10^100002-1)/9-10^33441 | 100002 | Akihiko Yoshida | 03/2018 |
| 9136 | (10^100002-1)/9-10^44692 | 100002 | Akihiko Yoshida | 03/2018 |
| 9137 | 10^100002-249519 | 100002 | Patrick De Geest | 07/2018 |
| 9138 | 10^100001+314199 | 100002 | Patrick De Geest | 07/2018 |
| 9189 | 25206!+p(4114) | 100001 | Henri Lifchitz | 09/2005 |
| 9190 | 25206!-p(5447) | 100001 | Henri Lifchitz | 10/2005 |
| 9191 | 25206!-p(12402) | 100001 | Henri Lifchitz | 04/2006 |
| 9192 | 25206!-p(16290) | 100001 | Henri Lifchitz | 09/2006 |
| 9193 | 25206!-p(19647) | 100001 | Henri Lifchitz | 02/2007 |
| 9194 | 2^332194+11473 | 100001 | Henri Lifchitz | 03/2007 |
| 9184 | 10^100000+342909 | 100001 | Milton L. Brown | 12/2007 |
| 9185 | 10^100000+346579 | 100001 | Robert Price | 04/2012 |
| 9186 | 10^100000+829767 | 100001 | Robert Price | 05/2012 |
| 9187 | 10^100000+871899 | 100001 | Robert Price | 05/2012 |
| 9188 | 10^100000+1475997 | 100001 | Robert Price | 07/2012 |
| 9177 | 10^100000+1751769 | 100001 | Robert Price | 08/2012 |
| 9178 | 10^100000+2155489 | 100001 | Robert Price | 10/2012 |
| 9179 | 10^100000+2483527 | 100001 | Robert Price | 12/2012 |
| 9180 | 10^100000+2503087 | 100001 | Robert Price | 12/2012 |
| 9181 | 10^100000+2686179 | 100001 | Robert Price | 12/2012 |
| 9182 | 10^100000+2688933 | 100001 | Robert Price | 12/2012 |
| 9183 | 10^100000+3667159 | 100001 | Robert Price | 08/2013 |
| 9158 | 10^100000+3938473 | 100001 | Robert Price | 05/2015 |
| 9159 | 10^100000+3979761 | 100001 | Robert Price | 05/2015 |
| 9160 | 10^100000+4293973 | 100001 | Robert Price | 09/2015 |
| 9155 | 10^100000+4858267 | 100001 | Robert Price | 12/2015 |
| 9156 | 10^100000+5113299 | 100001 | Robert Price | 02/2016 |
| 9157 | 10^100000+5169411 | 100001 | Robert Price | 02/2016 |
| 9147 | 10^100000+5354043 | 100001 | Robert Price | 05/2016 |
| 9148 | 10^100000+5717979 | 100001 | Robert Price | 05/2016 |
| 9149 | 10^100000+6080631 | 100001 | Robert Price | 07/2016 |
| 9150 | 10^100000+6308469 | 100001 | Robert Price | 07/2016 |
| 9151 | 10^100000+6512023 | 100001 | Robert Price | 08/2016 |
| 9152 | 10^100000+6596557 | 100001 | Robert Price | 08/2016 |
| 9153 | 10^100000+7115409 | 100001 | Robert Price | 10/2016 |
| 9154 | 10^100000+7235803 | 100001 | Robert Price | 10/2016 |
| 9164 | 10^100000+7867333 | 100001 | Robert Price | 12/2016 |
| 9165 | 10^100000+8743093 | 100001 | Robert Price | 02/2017 |
| 9166 | 10^100000+8955391 | 100001 | Robert Price | 03/2017 |
| 9167 | 10^100000+9180019 | 100001 | Robert Price | 03/2017 |
| 9168 | 10^100000+9225987 | 100001 | Robert Price | 04/2017 |
| 9169 | 10^100000+9265587 | 100001 | Robert Price | 04/2017 |
| 9170 | 10^100000+9287049 | 100001 | Robert Price | 04/2017 |
| 9171 | 10^100000+9425053 | 100001 | Robert Price | 05/2017 |
| 9172 | 10^100000+9450769 | 100001 | Robert Price | 05/2017 |
| 9173 | 10^100000+9528747 | 100001 | Robert Smith | 05/2017 |
| 9174 | 10^100000+9548071 | 100001 | Robert Price | 06/2017 |
| 9175 | 10^100000+10064287 | 100001 | Robert Price | 08/2017 |
| 9176 | 10^100000+10229569 | 100001 | Robert Price | 10/2017 |
| 9139 | 10^100000+11187931 | 100001 | Robert Price | 03/2018 |
| 9140 | 10^100000+11264721 | 100001 | Robert Price | 04/2018 |
| 9141 | 10^100000+11477661 | 100001 | Robert Price | 05/2018 |
| 9142 | 10^100000+11644653 | 100001 | Robert Price | 07/2018 |
| 9143 | 10^100001-431439 | 100001 | Patrick De Geest | 07/2018 |
| 9144 | 10^100000+11769399 | 100001 | Robert Price | 08/2018 |
| 9145 | 10^100000+11848159 | 100001 | Robert Price | 08/2018 |
| 9146 | 10^100000+11863467 | 100001 | Robert Price | 08/2018 |
| 9161 | 10^100000+11992051 | 100001 | Robert Price | 09/2018 |
| 9162 | 2^332196-1-2*29696 | 100001 | Matt Stath | 11/2018 |
| 9163 | 10^100000+12363957 | 100001 | Robert Price | 11/2018 |
| 9195 | 2^332196+1+2*17152 | 100001 | Matt Stath | 12/2018 |
| 9196 | 10^100000+12778033 | 100001 | Robert Price | 02/2019 |
| 9197 | 10^100000+13581679 | 100001 | Robert Price | 05/2019 |
| 9198 | 10^100000+13613199 | 100001 | Robert Price | 05/2019 |
| 9199 | 10^100000+13752327 | 100001 | Robert Price | 05/2019 |
| 9200 | 10^100000+14139243 | 100001 | Robert Price | 06/2019 |
| 9201 | 10^100000+14151057 | 100001 | Robert Price | 06/2019 |
| 9202 | 10^100000+14218923 | 100001 | Robert Price | 06/2019 |
| 9203 | 10^100000+24543147 | 100001 | Robert Price | 08/2021 |
| 9204 | 10^100000+24781659 | 100001 | Robert Price | 08/2021 |
| 9205 | 10^100000+24906153 | 100001 | Robert Price | 08/2021 |
| 9206 | 10^100000+25682679 | 100001 | Robert Price | 10/2021 |
| 9207 | 10^100000+25905301 | 100001 | Robert Price | 10/2021 |
| 9208 | 10^100000+25923967 | 100001 | Robert Price | 10/2021 |
| 9209 | 10^100000+26061691 | 100001 | Robert Price | 10/2021 |
| 9210 | 10^100000+26173351 | 100001 | Robert Price | 11/2021 |
| 9211 | 10^100000+26673487 | 100001 | Robert Price | 11/2021 |
| 9212 | 10^100000+26849359 | 100001 | Robert Price | 12/2021 |
| 9213 | 10^100000+26893887 | 100001 | Robert Price | 12/2021 |
| 9214 | 10^100000+26954551 | 100001 | Robert Price | 12/2021 |
| 9215 | 10^100000+27024543 | 100001 | Robert Price | 12/2021 |
| 9216 | 10^100000+27060877 | 100001 | Robert Price | 12/2021 |
| 9217 | 10^100000+27617577 | 100001 | Robert Price | 03/2022 |
| 9218 | 10^100000+27869671 | 100001 | Robert Price | 03/2022 |
| 9219 | 10^100000+27956481 | 100001 | Robert Price | 03/2022 |
| 9220 | 10^100000+28078261 | 100001 | Robert Price | 03/2022 |
| 9221 | 10^100000+28150203 | 100001 | Robert Price | 03/2022 |
| 9222 | 10^100000+28626021 | 100001 | Robert Price | 05/2022 |
| 9223 | 10^100000+28649299 | 100001 | Robert Price | 05/2022 |
| 9224 | 10^100000+29409799 | 100001 | Robert Price | 06/2022 |
| 9225 | 10^100000+29415577 | 100001 | Robert Price | 06/2022 |
| 9226 | 10^100000+29424201 | 100001 | Robert Price | 06/2022 |
| 9227 | 10^100000+29610153 | 100001 | Robert Price | 07/2022 |
| 9228 | 10^100000+30166789 | 100001 | Robert Price | 07/2022 |
| 9229 | 10^100000+30338259 | 100001 | Robert Price | 07/2022 |
| 9230 | 10^100000+30540031 | 100001 | Robert Price | 07/2022 |
| 9231 | 10^100000+30635157 | 100001 | Robert Price | 07/2022 |
| 9232 | 10^100000+30762711 | 100001 | Robert Price | 07/2022 |
| 9233 | 10^100000+30862057 | 100001 | Robert Price | 07/2022 |
| 9234 | 10^100000+30998953 | 100001 | Robert Price | 07/2022 |
| 9235 | 10^100000+31405203 | 100001 | Robert Price | 07/2022 |
| 9236 | 10^100000+40159119 | 100001 | Robert Price | 07/2022 |
| 9237 | 10^100000+40181863 | 100001 | Robert Price | 07/2022 |
| 9238 | 10^100000+40277131 | 100001 | Robert Price | 07/2022 |
| 9239 | 10^100000+40326061 | 100001 | Robert Price | 07/2022 |
| 9240 | 10^100000+40417411 | 100001 | Robert Price | 07/2022 |
| 9241 | 10^100000+50049909 | 100001 | Robert Price | 07/2022 |
| 9242 | 10^100000+50510163 | 100001 | Robert Price | 07/2022 |
| 9243 | 10^100000+50591583 | 100001 | Robert Price | 07/2022 |
| 9244 | 10^100000+50850357 | 100001 | Robert Price | 07/2022 |
| 9245 | 10^100000+50974641 | 100001 | Robert Price | 07/2022 |
| 9246 | 10^100000+51046671 | 100001 | Robert Price | 07/2022 |
| 9247 | 10^100000+51459657 | 100001 | Robert Price | 07/2022 |
| 9248 | 10^100000+70081471 | 100001 | Robert Price | 07/2022 |
| 9249 | 10^100000+70159557 | 100001 | Robert Price | 07/2022 |
| 9250 | 10^100000+70262479 | 100001 | Robert Price | 07/2022 |
